Mathematical Concepts of Quantum Mechanics: Edition 3

Stephen J. Gustafson · Israel Michael Sigal

oct 2020 · Springer Nature

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The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline.

Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content.

It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include: many-body systems, modern perturbation theory, path integrals, the theory of resonances, adiabatic theory, geometrical phases, Aharonov-Bohm effect, density functional theory, open systems, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group.

With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. Some of the sections could be used for introductions to geometrical methods in Quantum Mechanics, to quantum information theory and to quantum electrodynamics and quantum field theory.

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Stephen J. Gustafson is Professor of Mathematics at the University of British Columbia. His research centres on various partial differential equations arising in physics.
Israel Michael Sigal is the Norman Stuart Robertson chair in Applied Mathematics at the University of Toronto. He works in several areas of mathematical physics and applied mathematics.